There are two State Parks with easy access to Chicago:
1. Illinois Beach SP in Beach Park (the next town North of Waukegan).
2. Chain o' Lakes SP near Spring Grove/Fox Lake.
Commuter train service (METRA) is available from both parks. As previously stated; DO NOT try to drive in Chicago.
Metra offers a "weekend pass" for $7.50 (unlimited rides).
While you are in the area, take the train out to Oak Park where you can take a walking tour of my paper route (almost every house was designed by Frank Lloyd Wright).
Edit to add:
"Trucks and RVs are not allowed on Lake Shore Drive or any 'Boulevard'"